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AN  INTERFERENCE  METHOD  FOR  THE 
MEASUREMENT  OF  THE  SPEED  OF  SOUND 
IN  LIQUIDS. 


BY 


LLOYD   BALDERSTON,   JR. 


Thesis  presented  to  the  Faculty  of  Philosophy 
of  the  University  of  Pennsylvania  in  partial 
fulfillment  of  the  requirements  for  the  degree 
of  Ph.  D. 


Randal  Morgan  Laboratory  of  Physics. 
1904. 


AN  INTERFERENCE  METHOD  FOR  THE 
MEASUREMENT  OF  THE  SPEED  OF  SOUND 
IN  LIQUIDS. 


BY 


LLOYD    BALDERSTON,   JR. 

M 


Thesis  presented  to  the  Faculty  of  Philosophy 
of  the  University  of  Pennsylvania  in  partial 
fulfillment  of  the  requirements  for  the  degree 
of  Ph.  D. 


Randal  Morgan  Laboratory  of  Physics. 


1904. 


AN  INTERFERENCE  METHOD  FOR  THE  MEASURE- 
MENT OF  THE  SPEED  OF  SOUND 
IN  LIQUIDS. 

THE  speed  of  propagation  of  sound  waves  in  air  has  been  ex- 
tensively investigated  both  mathematically  and  experiment- 
ally. Newton  ( i )  showed  that  in  an  elastic  fluid  pulses  are  propa- 
gated with  a  speed  proportional  directly  to  the  square  root  of  the 
elasticity  (vis  elastica)  and  inversely  to  the  square  root  of  the 
density.  He  deduces  for  the  speed  under  standard  conditions  the 
value  979  feet  per  second,  which  is  much  too  low,  and  the  hypothesis 
which  he  proposed  as  an  explanation  of  the  discrepancy  was  soon 
shown  to  be  untenable. 

This  problem,  finally  solved  by  Laplace,  (2)  furnishes  one  of 
the  most  interesting  chapters  in  the  history  of  physical  science. 
Laplace  showed  that  the  heat  developed  by  compression  was  the 
cause  of  the  discrepancy  between  Newton's  value  and  the  true  one. 

He  proved  that  ~-  —  -=£  where  E<$>  is  the  adiabatic  and  E  Q  the 
ZTe      Cv 

isothermal  elasticity,  Cp  the  specific  heat  at  constant  pressure  and 
Co  that  at  constant  volume.  The  ratio  of  the  specific  heats  is 
practically  constant  for  diatomic  gases,  and  is  commonly  denoted 
by  K.  Laplace's  correction  factor  is  therefore  VK'—'  VT^  —  //? 
nearly. 

The  academicians  of  Florence  in  the  i7th  century,  having  ex- 
perimented with  water  enclosed  in  silver  spheres,  concluded  that 
it  was  incompressible.  Hence  it  was  concluded  that  water  was  not 
elastic  and  could  not  transmit  sound  waves.  John  Canton,  how- 
ever, showed  before  the  Royal  Society  in  1762  that  water  can  be 
compressed,  and  Franklin  afterward  experimented  on  the  trans- 
mission of  sound  through  water.  The  field  thus  opened  has  been 
much  less  fully  investigated  than  that  in  which  gases  are  involved. 

When  Laplace  had  supplied  the  correction  to  Newton's  for- 
mula, the  question  arose  whether  or  not  any  such  factor  must  be 

(1)  Principia,  Book  II,  Prop.  48,  49,  50. 

(2)  Mecanique  Celeste,  Vol.  V,  Book  XII,  Ch.  3,  Sect   I. 


165259 


used  in  the  ca^  of  liquids.  This  problem  was  attacked  in  a  number 
of  ways  by  different  investigators.  Colladon  and  Sturm  (  I  )  of 
Geneva  made  direct  experiments  en  the  development  of  heat  by  cofn- 
pression.  In  the  case  of  ether,  a  blow  producing  compression  equal 
to  that  due  to  a  pressure  of  40  atmospheres  caused  a  rise  of  6  de- 
grees C.  in  temperature.  A  like  blow  in  the  case  of  water  produced 
no  perceptible  effect.  They  then  undertook  to  determine  the  speed 
of  sound  in  free  water,  in  order  to  compare  the  actual  speed  with 


that  deduced  from  the  formula  v=\L     where  £Q    is  the  isother- 

P 
mal   elasticity  and    p    the  density.     The   two  results   agreed   very 

closely.  They  therefore  concluded  that  in  the  propagation  of  sound 
waves  in  water,  thermal  effects  due  to  the  disturbance  do  not  per- 
ceptibly influence  the  speed. 

The  measurements  were  made  on  Lake  Geneva  in  the  autumn  of 
1826.  The  two  stations  selected  were  13487  meters  apart,  (with 
a  possible  error  of  20  meters).  A  bell  70  cm.  high  and  slightly  less 
in  diameter,  suspended  in  the  water  at  the  depth  of  a  meter,  was 
struck  by  a  hammer.  A  'torch  was  so  connected  to  the  lever  carry- 
ing the  hammer  that  it  fired  a  charge  of  powder  at  the-  same  instant 
that  the  bell  was  struck.  The  observer  at  the  other  station  was 
provided  with  a  quarter-second  stop-watch  and  a  trumpet,  suitably 
placed  to  catch  the  sound  from  the  bell.  The  experiments  were 
conducted  at  night.  The  mean  temperature  of  the  water  was  8.1 
degrees  and  the  average  depth  between  the  stations  140  metefs. 
The  water  contained  167  parts  per  million  total  solids  and  .034 
volume  of  air. 

Forty-four  observations  of  the  time  between  the  flash  and  the 
sound  gave  results  varying  from  9  to  9^2  seconds,  with  a  mean  of 
9.4.  This  gives  as  the  mean  value  of  the  speed,  1435  meters  per 
second.  The  minimum  value,  obtained  by  using  the  greatest  ob- 
served time  and  least  possible  distance,  was  1417  meters;  and  the 
maximum,  obtained  in  a  like  manner,  1500  meters  per  second.  The 
extreme  variation  thus  amounts  to  nearly  6  per  cent,  of  the  total. 
The  best  data  available  at  that  time  for  the  compressibility  of  water 
gave  for  the  calculated  value  1428  meters.  More  recent  data  in- 
crease this  to  1437,  showing  a  concordance  which  is  really  remark- 
able. The  authors  refer  in  their  memoir  to  a  measurement  made 

(i)     Annales  de  Chemie  et  de  Physique,  Series  2,  Vol.  36.  (1827). 

2 


"a  few  years"  before  by  M.  Beudant  in  sea-water  at  Marseilles  as 
the  only  experiment  which  had  previously  been  tried.  The  method 
used  was  not  very  exact.  Beudam's  result  was  1500  meters. 

A  long  series  of  experiments  on  the  speed  of  sound  was  con- 
ducted by  M.  G.  Wertheim  (i)  at  Paris.  His  method  was  indirect 
He  immersed  organ  pipes  in  water  and  sounded  them  by  forcing 
a  current  of  water  through  them.  The  note  was  determined  by 
comparison  with  a  sonometer.  Varying  the  pressure  under  which 
the  water  was  forced  through  the  pipes  caused  them  to  give 
different  harmonics.  From  these  the  pitch  of  the  fundamental  was 
calculated.  Certain  corrections  depending  on  the  shape  and  diameter 
of  the  pipe  having  been  applied,  the  speed  of  sound  in  the  liquid  was 
obtained  by  multiplying  the  wave-length  by  the  vibration  number. 
The  mean  of  58  experiments  at  temperatures  between  15  and  20 
degrees  was  1173.4  meters  per  second. 

This  is  much  below  the  absolute  value,  if  we  may  so  call  the 
speed  in  free  water.  Wertheim  reasoned  that  the  column  of  water 
in  the  tube  behaved  like  a  rod  of  metal.  A  part  of  the  energy  of 
the  source  is  transmitted  along  the  rod  and  a  part  is  communi- 
cated to  the  surrounding  medium  by  the  lateral  motion  of  the  sides 
of  the  bar.  The  rod  being  thus  free  to  expand  laterally,  a  blow  on 
the  end  will  manifestly  be  propagated  less  rapidly  than  would  a  dis- 
turbance moving  from  a  point  in  an  infinite  mass  of  the  metal. 
Wertheim  calculated  that  the  speed  in  free  water  would  be  greater 
than  in  a  column  of  water  contained  in  a  tube  in  the  ratio  of  -y  3*'\2* 
Multiplying  his  result  by  this  ratio  he  obtained  the  value 
1437  meters  per  second,  precisely  that  given  by  theory  from  the 
compressibility  at  the  temperature  8  degrees.  He  does  not  give 
the  temperature  for  each  experiment  of  the  58  but  says  that  they 
were  all  carried  out  at  temperatures  between  15  and  20  degrees. 
The  result  1173.4  is  given  in  his  summary  as  for  15  degrees. 

Wertheim  also  experimented  with  various  solutions  in  water, 
with  alcohol,  turpentine  and  ether,  and  with  water  at  various  tem- 
peratures. His  values  for  water  at  30,  40,  50  and  60  degrees  are  each 
based  on  five  or  six  observations,  the  extremes  differing  in  each  case 
by  more  than  100  meters,  with  a  probable  error  of  about  i  per 
cent.  In  the  table  are  given  his  values  in  column  A,  the  same  multi- 
(i)Annales  de  Cheinie  et  de  Physique,  Series  3,  Vol.  23,  (1848). 


plied  by      |/i{     in  column  B,  while  in  column  C  are  the  values  cal- 
culated from  the  elasticity  and  density,  including  the  correcting^  fac- 

tor  V5? 
Cv 

Temp.  ABC 

30°  1250.9  1528. 5/  1529-5 

40°  1324-8  1622.5  1664.5 

50°  i349.o  1652.0  1601.3 

6o°v  1408.2  J724«7  1622.6 

70°  1639.3 

80°  1650.4 

The  method  of  stationary  waves  devised  by  Kundt  for  meas- 
uring the  speed  of  sound  propagation  in  solids  and  gases,  he  has 
applied  also  to  liquids,  (i)  He  used  six  glass  tubes,  differing  in 
internal  diameter  and  thickness  of  wall.  The  powder  used  was  of 
iron.  His  results  were  fairly  concordant.  Assuming  that  in  the 
neighborhood  of  20  degrees  the  speed  of  sound  in  free  water  in- 
creases 4  m.  per  second  for  each  degree  increase  of  temperature, 
and  reducing  Kundt's  results  to  20  degrees,  they  vary  from  about 
1044  m.  for  a  tube  22  mm.  thick  and  28  mm.  in  diameter  to  1375 
m.  for  one  5  mm.  thick  and  14  mm.  in  diameter.  He  concluded  that 
the  speed  is  dependent  on  the  diameter  of  the  tube  and  the  thick- 
ness of  the  walls,  quoting  a  passage  from  Helmholtz  (2)  in  sup- 
port of  this  view. 

Threlfall  and  Adair  (3)  experimented  on  the  speed  of  propaga- 
tion in  water  of  waves  due  to  explosions,  in  the  harbor  of  Port 
Jackson,  Australia.  They  used  charges  of  gun  cotton  of  various 
sizes.  The  distance  was  less  than  250  meters,  and  the  measure- 
ment of  time  was  made  by  a  special  form  of  chronograph.  They 
found  values  varying  with  the  quantity  of  explosive  used,  the  high- 
est being  2013  meters  per  second. 

Professor  Tito  Martini  (4)  conducted  an  extensive  research  on 

Chis  subject  in  1884-5.     His  method  was  based  on  the  sounds  pro- 
luced  by  the  efflux  of  water  from  tubes,  a  phenomenon  first  de- 

(f)  Poggendorfs  Annalen,  (1874),   Vol.  153,  p.  I. 

(2)  Fortschritte  der  Physik,  1848,  P.  114. 

(3)  Proc.  Royal  Soc.  1889,  Vol.  XI/VI,  P.  496. 

(4)  Atti  del  Reale  Instituto  Vencto,  Series  VI.  Vol.  IV,  Appendix. 


scribed  by  Savart  (i)  in  a  posthumous  memoir  presented  to  the 
Paris  Academy  by  Arago  in  1853.  Martini  used  a  tube  of  glass 
or  brass,  the  end  being  closed  by  a  brass  plate  25  mm.  thick  with 
a  hole  2.5  mm.  in  diameter  in  the  middle.  Water  flowed  into  the 
tube  from  a  reservoir.  He  found  difficulty  in  regulating  the  inflow 
so  as  to  maintain  a  constant  level  while  the  water  was  flowing,  out 
at  the  bottom.  T6  obviate  this,  the  water  was  conveyed  by  means 
of  a  rubber  hose  to  the  bottom  of  the  tube,  where  it  flowed  in 
through  the  opening,  overflowing  at  the  top.  The  rate  of  flow  was 
controlled  by  a  stopcock.  When  the  liquid  column  in  the  upright 
tube  reached  a  height  of  from  18  to  20  cm.  the  note  began,  and 
fell  in  pitch  as  the  column  lengthened.  The  pitch  was-  measured 
by  the  same  method  which  Wertheim  had  used,  a  sonometer  being 
tuned,  .to  unison  with  the  note  given  by  the  water  tube,  and  the 
pitch  calculated  from  the  length  of  the  string. 

Using  glass  tubes  of  various  lengths  but  the  sWie  diameter 
(3  cm.),  he  found  that  the  vibration  period  was  not  proportional 
to  the  length  of  the  tube.  In  the  case  of  a  tube  whose  gravest 
mode  of  vibration  gives  a  certain  note,  if  we  assume  the  length  of 
the  tube  to  be  ^  the  wavelength  of  that  note,  the  speed  of  sound 
in  water  will  be  four  times  the  product  of  the  vibration  number  by 
the  length  of  the  column.  Proceeding  in  this  manner  Martini  ob- 
tained values  -at  4.7  degrees  varying  from  1394  meters  for  a  tube 
207  mm.  long  to  1592  for  one  546  mm.  in  length.  The  value  1435 
m.  identical  with  that  found  by  Colladon  and  Sturm  by  direct  meas- 
urement at  8.1  degrees, was  given  by  a  tube  30  cm.  long.  Martini 
therefore  assumed  that  tubes  whose  length  is  10  times  their  di- 
ameter will  give  by  this  method  absolute  values  for  the  speed  of 
sound  in  liquids.  In  his  further  experiments  on  water  he  used 
five  br^ss  tubes,  each  having  its  length  and  diameter  in  the  ratio 
10:1.  He  also  worked  with  alcohol,  ether,  kerosene  and  several 
water  solutions.  The  results  for  water  at  various  temperatures 
are  given  in  the  table: 

(r)     Comptes  Rendus ;  August,  1853. 

5 


Mean.          Probable 
Meters  sec.    Error,  m. 

1398.6  11.3 


1409.0  6.7 


1437.3  10.1 


1457.2  8.0 


An  important  contribution  to  the  mathematical  theory  of  the 
propagation  of  sound  waves  in  liquids  was  made  by  Clausius,  who 
showed"  (  L)  that  the  specific  heats  are  connected  by  the  relation 

Cp  -  Cz'__a*   ®        ,  where  a  is  the  coefficient  of  volume  increase  with 

/ 
temperature,  9     is  the  absolute  temperature,     p      the  density  and 

the   elasticity   at  constant   temperature.     As   in   the   case   of 


Temperature 
C. 

Length  of 
Column,  cm. 

Speed  of 
Sound  m. 

3V 

60 
50 
40 
30 

1353-2 
1435-7 
1383-8 
1422.0 

7.6° 

60 
40 
30 

20 

1374-5 
1407.5 
1442.0 
1412.0 

I3.70 

60 
50 
40 

30 

1399.4 
H54-5 
1429.0 

1466  2 

25.2° 

\ 

60 

50 
40 

30 

1432.0 
I47I.2 
1442.2 
1482.6 

gases,  V=  and  =          In  liquids,  however,  is  not 

Cv  Lv 


constant.     At  4°   a  —  O    and    ~    =  /.  As  the  temperature 

Cv 

rises  <£    increases.     Since  the  work  of  Colladon   and  Sturm  was 
Cv 

done  in  water  at  8.1  degrees,  for  which  temperature  the  correction 

factor    V—   scarcely  differs  from  I,  it  is  not  surprising  that  they 

Cv 

found  no  correction  factor  necessary.  Their  determination  is  the 
only  direct  measurement  of  the  speed  of  sound  in  fresh  water 
which  has  found  a  place  in  our  scientific  literature.  Their  result 


no  doubt  merits  the  confidence  which  it  has  received )  but  with  our 
improved  methods  of  time  measurement  it  is  certainly  worth  while 
to  repeat  the  work.  At  least  two  determinations  should  be  made, 
at  temperatures  as  widely  different  as  possible. 

The  various  laboratory  methods  which  have  been  employed 
are  necessarily  indirect,  and  in  most  cases  the  results  obtained 
were  not  assumed  to  be  absolute  values.  Wertheim's  method  has 
a  limit  of  error  as  high  as  4  per  cent.  Even  if  this  could  be  made 
much  less,  the  method  would  still  be  unreliable  in  so  far  as  concerns  f 
absolute  results,  for  Kundt's  work  has  shown  thatV  in  liquid  col-  / 
umns  in  tubes  is  a  function  of  the  diameter  of  the  tube  and  the 
thickness  of  its  wall.  Wertheim's  correction  factor,  A  ~  is  thus  ' 
proved  to  have  no  logical  basis.  Helmholtz  showed  in  the  article 
before  referred  to,  that  columns  of  liquid  in  tubes  cannot  behave 
like  rods  of  metal,  since  the  liquid  is  not  entirely  free  to  expand 
laterally.  The  diminished  speed  in  the  tube,  as  compared  with  free 
water,  is  due  to  the  yielding  of  the  walls  of  the  tube,  and  the 
diminution  is  greater  as  the  walls  are  made  thinner.  In  so  far 
as  accuracy  of  measurement  is  concerned,  Martini's  method  appears 
to  possess  little  advantage  over  Wertheim's.  He  assumed  that  his 
results  were  absolute  values,  but  the  assumption  seems  to  rest  on 
a  rather  doubtful  basis. 

A  laboratory  method  giving  relative  results  only  might  be  use- 
ful in  confirming  the  theoretical  values  at  higher  temperatures  and 
in  investigating  other  liquids.  The  experiments  here  described  were 
made  in  an  attempt  to  devise  a  method  based  on.  interference.  The 
plan  adopted  is  that  shown  in  the  figure. '  The  sources  are  tele- 
phone diaphragms  A,  A',  5  cm.  in  diameter,  supported  between  rub- 
ber gaskets  and  presenting  a  free  surface  3.8  cm.  in  diameter. 
These  are  actuated  by  the  electro-magnets  B,  Bx,  through  which 
an  intermittent  current  passes.  These  magnets  have  cores  of  Nor- 
way iron  6.4  mm.  in  diameter  and  8.5  cm.  long,  and  are  wound 
with  720  turns  each  of  No.  18  wire.  The  sliding  joint  C  permits  an 
extension  of  80  cm.  At  D  and  D'  the  brass  tube,  3.8  cm.  external 


B 

(Two  meters  of  the  longer  tube  are  omitted.) 


diameter  and  1.6  mm.  wall,  is  discontinuous,  being  joined  by  a 
piece  of  rubber  hose  for  the  purpose  of  sound-insulation.  The 
brass  Y  marked  E  is  joined  to  the  two  tubes  by  rubber  connections, 
and  is  extended  by  another  piece  of  rubber  hose,  F,  bent  up  to 
prevent  the  escape  of  the  water.  The  brass  tubes  are  supported 
on  a  board  5  m.  long,  the  parts  E  and  F  being  suspended  by  rubber 
bands  to  a  projecting  arm,  so  as  to  insulate  them  as  well  as  possible 
from  the  table.  With  the  idea  of  preventing  the  transmission  of 
sound  by  the  walls  of  the  tube,  rubber  hose  was  at  first  used  from 
D  to  E.  The  amount  of  energy  received  at  E  from  the  more  distant 
source  was  insignificant,  most  of  it  being  dissipated  through  the 
vielding  walls  of  the  tube. 

If  now  two  sounds  of  the  same  pitch  and  in  the  same  phase 
are  produced  at  A  and  A'  and  their  intensity  i>e  so  adjusted  that 
they  produce  equal  effects  at  F,  there  should  be  destructive  inter- 
ference when  the  distances  of  the  two  sources  from  F  differ  by  a 
half  wave-length.  The  intermittent  current  was  at  first  furnished 
by  a  device  similar  to  the  commutator  of  an  ordinary  dynamo,  car- 
ried on  the  spindle  of  a  small  motor.  One  brush  touches  a  solid 
brass  ring.  The  other  is  alternately  in  contact  with  brass  and  fibre. 
A  switch  placed  conveniently  near  the  observing  end  sent  current 
through  one  magnet  or  the  other  or  both  in  parallel.  It  was  found 
that  when  both  sources  were  acting  there  were  present  overtones  of 
considerable  amplitude  which  were  not  heard  when  one  source  only 
was  in  operation.  This  effect  seems  to  have  been  due  to  mutual 
inductive  action  of  the  two  sources.  While  the  current  from  the 
battery  was  interrupted  the  electro-magnets  being  connected  in 
parallel  were  on  a  closed  circuit  of  their  own.  The  residual  mag- 
netism present  in  the  core  during  the  brief  interval,  and  the  over- 
tones of  the  diaphragm  made  of  each  source  a  telephonic  trans- 
mitter, while  the  other  acted  as  a  receiver.  The  effect  was  thus 
cumulative,  and  the  quality  of  the  sound  when  both  sources  were 
acting  was  conspicuously  different  from  that  of  the  sound  from  a 
single  source.  This  difficulty  was  obviated  by  placing  the  sources 
in  series  and  providing  a  third  coil  exactly  similar  to  the  other 
two  which  could  be  connected  in  series  with  either  of  them  and 
cut  out  when  the  sources  were  both  in.  Thus  the  intensity  of  the 
current  was  the  same,  whether  one  or  both  magnets  were  acting. 


The  necessary  connections  were  arranged  by  means  of  a  special 
three  point  switch. 

The  rate  of  interruption  of  the  current  was  ascertained  by 
means  of  a  speed  counter  attached  to  the  motor.  This  rings  a  bell 
at  intervals  of  382^  revolutions  of  the  armature,  and  as  the  in- 
terrupting disk  has  8  brass  sectors,  each  tap  of  the  bell  corres- 
ponds to  3060  vibrations.  Sparking  of  the  interrupter  was  pre- 
vented by  placing  an  adjustable  condenser  across  the  break.  In  or- 
der to  get  a  reasonably  pure  tone,  the  interrupter  must  be  accur- 
ately made  and  kept  clean  and  the  brushes  must  fit  neatly  on  its 
surfaces. 

It  is  necessary  to  have  the  apparatus  completely  filled  with 
water,  without  air  bubbles.  A  small  bubble  near  one  of  the 
diaphragms  interferes  seriously  with  the  intensity  of  the  sound 
transmitted  through  the  water.  In  order  to  avoid  bubbles,  the 
water  was  boiled  and  put  into  the  apparatus  while  still  hot,  so  that 
in  cooling  it  might  absorb  any  air  which  had  adhered  to  the  walls 
of  the  tube. 

At  first  the  apparatus  was  closed  at  E  by  the  diaphragm  of  a 
multiple  contact  microphone.  A  reservoir  communicating  with  the 
long  tube  by  a  small  hole  was  placed  near  D  to  supply  water  to  keep 
the  tube  full  when  the  length  was  increased  The  microphone 
receiving  apparatus  was  not  satisfactory,  probably  on  account  of 
confused  multiple  reflections  of  overtones  from  the  diaphragm  and 
the  walls  of  the  tube.  The  form  shown  in  the  figure  was  after- 
ward adopted.  The  reservoir  was  discarded  and  the  levej  of  the 
water  kept  nearly  constant  by  pouring  in  more  when  the  tube  is 
longer.  The  adjustment  of  the  length  of  the  tube  is  made  by 
means  of  a  lever  at  the  observing  end,  attached  to  a  rod  which 
in  turn  is  secured  to  the  carriage  of  the  sliding  portion  by  a  clamp. 
Observations  are  made  simply  by  placing  the  ear  at  the  end  of 
the  tubeF  Of  course  reflection  takes  place  at  the  air  surface,  but 
much  less  intense  than  in  the  case  of  the  diaphragm,  and  the  re- 
flected waves  are  so  scattered  on  account  of  the  obliquity  of  the 
surface  that  they  hinder  observation  but  little. 


The  motor  used  is  of  the  series  type,  and  was  driven  by  from 
12  to  1 6  storage  cells.  The  conditions  were  kept  apparently  con- 
stant, but  the  speed  of  the  motor  varied  slightly.  It  seemed  prob- 
able that  this  variation  was  the  cause  of  the  difficulty  in  obtaining 
sharply  defined  minima.  A  small  fan  with  pivoted  spring-held 
blades  was  put  on  the  spindle  of  the  motor  to  act  as  a  governor,  but 
proved  inefficient. 

In  order  to  secure  constancy  in  the  pitch  of  the  sources,  a 
vibrating  interrupter  was  substituted  for  the  rotary  one.  A  steel 
bar  was  clamped  to  a  heavy  iron  base  and  kept  in  vibration  in  the 
same  manner  as  an  electrically  driven  tuning  fork.  The  end  of 
the  bar  carries  a  platinum  point  which  dips  into  mercury  and  so 
interrupts  the  current  which  passes  to  the  sources.  The  vibrator 
works  very  well  when  driven  by  two  cells  of  storage  battery.  The 
current  which  passes  to.  the  electromagnets  B  and  B  is  furnished 
by  four  storage  cells.  The  vibrator  was  tuned  by  comparison  with 
a  Konig  fork  to  192  vibrations  per  second,  in  order  that  a  resonator 
responding  to  that  note  might  be  used  in  listening  at  F.  The  object 
of  this  was  to  get  rid  of  the  overtones  which  helped  to  mask  the 
minima. 

The  platinum  point  which  dips  into  the  mercury  was  attached 
to  a  slender  brass  spring,  tuned  to  the  same  pitch  as  the  vibrator  in 
order  to  secure  greater  amplitude.  The  spring  was  about  35  mm. 
long,  and  its  amplitude  at  the  free  end  was  as  great  as  3  mm., 
about  10  times  that  of  the  end  of  the  vibrator  bar  to  which  it  was 
screwed.  Such  an  amplitude,  was  not  only  not  necessary,  it  was 
not  satisfactory,  drops  of  mercury  being  thrown  out  of  the  cup  by 
the  platinum  tip.  The.  brass  spring  was  discarded  and  another 
made  whose  natural  period  was  about  \y2  times  as  great.  This 
gave  sufficient  amplitude,  about  .6  mm.,  but  the  pitch  of  the  vibrator 
rose  about  12  vibrations  per  second  when  the  change  had  been  made. 
The  first  spring  weighed  i  gram,  the  other  .83  grams.  In  order 
to  see  whether  the  difference,  in  weight  could  account  for  the 
change  of  pitch,  one  of  the  screws  by  which  the  spring  was  at- 
tached to  the  bar  was  taken  out.  Its  removal  changed  the  pitch 
by  less  than  half  a  vibration  per  second.  The  screw  weighed  .27 
gram.  The  part  of  the  bar  in  vibration  weighs  about  90  grams.  It 
is  evident  that  the  retarding  effect  of  the  first  spring  was  largely 
due  to  its  synchronism  with  the -bar. 

10 


It  was  difficult  to  make  this  interrupter  work  smoothly.  It  has 
a  tendency  to  spark  explosively  at  unexpected  moments,  in  spite 
of  carefully  adjusted  condenser  capacity.  Six  or  eig-ht  storage 
cells  may  be  be  used  with  the  rotary  interrupter,  giving  a  current  of 
three  or  four  amperes  through  the  sources,  but  the  vibrator  does 
not  work  well  with  more  than  four  cells.  The  tones  obtained  were 
not  so  pure  as  those  given  by  the  other  device,  but  the  resonator 
was  expected  to  eliminate  the  overtones.  This  hope,  however, 
proved  illusory.  The  vibrations  sent  out  into  the  air  of  the  room 
by  various  parts  of  the  apparatus,  particularly  by  the  longer  brass 
tube,  so  affected  the  sensitive  resonator  that  it  was  practically  use- 
less. The  vibrator  had  been  put  in  a  closet  on  a  pad  of  cotton  so 
that  it  did  not  contribute  to  the  diffused  sound  which  affected  the 
resonator.  The  overtones  in  the  sound  transmitted  through  the 
water  made  it  very  difficult  to  locate  the  minima  at  all  closely.  The 
invariability  of  the  note  also  introduced  a  difficulty  because  it  was 
hard  to  avoid  being  influenced  by  the  previous  readings.  The 
region  within  which  the  minimum  lay  could  be  located  quite  easily, 
but  over  a  space  of  twelve  or  fifteen  centimeters  the  variation  was 
very  slow. 

On  account  of  the  greater  purity  of  the  sounds  obtained,  the 
motor  interrupter  was  again  tried.  'Another  motor  was  selected, 
having  a  better  balanced  armature,  but  it  was  no  more  uniform 
in  speed  than  the  other.  A  regulating  fan,  of  the  type  already  de- 
scribed but  much  larger,  was  connected  to  the  motor  by  a  belt.  The 
driving  current  was  then  adjusted  to  give  about  192  vibrations,  so 
that  the  constancy  of  the  pitch  could  be  tested  by  comparison  with 
the  standard  fork.  The  note  was  found  to  vary  two  or  three  vibra- 
tions per  second,  rising  and  falling  from  one  to  four  times  per 
minute. 

The  results  so  far  obtained  are  given  in  the  table  which  fol- 
lows. Observations  i  to  4  were  taken  with  the  vibrating  inter- 
rupter, the  others  with  the  rotary  one.  To  make  the  results  more 
easily  comparable  they  are  reduced  to  20  degrees  by  adding  or 
subtracting  3.2  meters  for  each  degree  below  or  above  20  degrees. 
The  values  found  are  about  .8  of  that  for  free  water.  The  cor- 
rection used  is  therefore  .8x4  meters, 

II 


No. 
i 

2 

3 
4 
5  ' 
6 

7 
8 

9 
10 
ii 

12 
13 


n=vibration  frequency. 

d=rdistance  between  sources,  cm. 

t=temperature,  centigrade. 

v=  speed  of  propagation,  meters  per  sec. 

v20=speed  reduced  to  20  degrees. 


192 
192 
192 
192 
170 
178 
187 

193.7 

200.5 

185.2 

189. 

192. 

192. 


313- 
3*4- 
351.5 
336.5 


316. 

306.5 

323- 


318.5 
317- 


t 

V 

V20 

20.3 

1203.8 

I2O2.8 

20. 

1205.8 

1205.8 

20. 

I20I.9 

I2OI-9 

21.4 

1205.8 

1201.3 

15.8 

II95.I 

1208.5 

18.6 

1197  9 

1202.4 

18.5 

i  191.2 

1196.0 

16.3 

1224.0 

I235-8 

16.3 

1229.0 

1240.8 

21.2 

1  196.4 

1192  6 

20. 

1205.8 

1205.8 

20.5 

1223  o 

1221.4 

20-5 

1217.3 

1215-7 

Mean 

1210.6 

The  uncertainty  introduced  by  variation  of  the  speed  of  the 
motor  amounts  to  \y2  per  cent,  of  the  quantity  measured.  Two 
other  causes  contribute  to  make  the  minima  difficult  to  fix  with  ac- 
curacy. Some  sound  is  conveyed  to  the  ear  by  the  solid  parts  of 
the  apparatus.  Some  confused  sound  is  also,  conveyed  by  the 
water  itself.  This  last  difficulty  results  from'  the  fact  that  every 
part  of  the  tubes  acts  as  a  source  of  sound.  When  a  condensation 
is  sent 'out  from  the  source,  it  sets  up  lateral  vibrations  in  the  walls 
of  the  tube.  These  waves  travel  along  the  tube  at  a  rate  different 
from  that  of  the  sound  wave  in  the  water,  and  the  vibrations  set  up 
in  the  water  by  the  walls  of  the  tube  arrive  at  the  point  of  observa- 
tion in  all  phases.  Sound  of  the  fundamental  pitch  due  to  these 
two  causes  is  thus  heard  at  F  when  the  two  main  sources  are  in  in- 
terference. 


It  will  be  seen  that  the  method  is  capable  of  a  degree  of  accur- 
acy as  great  as  that  given  by  other  indirect  methods,  even  with  the 
imperfect  apparatus  employed.  By  using  a  phonic  wheel  (i)  or 
other  device  to  give  uniform  speed  to  the  interrupter,  and  by  more 
perfect  insulation  of  the  apparatus,  it  is  hoped  that  a  much  higher 
degree  of  accuracy  can  be  reached.  Another  point  which  needs 
to  be  improved  is  the  action  of  the  diaphragms.  Those  which  were 
used  were  very  erratic.  Both  quality  and  loudness  of  the  tone  were 
subject  to  sudden  changes  without  apparent  cause,  necessitating 
frequent  readjustment.  Special  diaphragms  can  probably  be  de- 
vised which  will  be  better. 

Several  possible  sources  of  constant  error  have  not  been  in- 
vestigated. Perhaps  the  most  important  of  these  is  lack  of  exact 
coincidence  of  phase  in  the  sources.  In  so  far  as  this  might  result 
from  differences  in  the  magnets  it  could  be  eliminated  by  inter- 
changing them.  But  it  might  result  also  from  differences  in  the 
diaphragms  and  in  the  distance  between  diaphragm  and  magnet 
pole.  Such  differences  could  be  detected  by  optical  methods. 


(i)     Lord  Rayleigh's  Scientific  Papers,  Vol.  II,  Pages  179-180. 

13 


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